Question: If $y = \displaystyle\frac{1}{3x+1}$, what is the value of $x$ when $y = 1$?
Since $y=1$, we have $1 =\displaystyle\frac{1}{3x+1}$.  Multiplying both sides by $3x+1$, we have $$3x+1=1$$ $$\Rightarrow \qquad 3x=0$$ $$\Rightarrow \qquad x=\boxed{0}$$